幻影对齐强度猜想：利用图匹配对齐强度来指示有意义的图匹配的实际应用
The Phantom Alignment Strength Conjecture: Practical use of graph matching alignment strength to indicate a meaningful graph match
AI总结：
本文提出“幻影对齐强度猜想”，旨在区分因随机噪声产生的误导性幻影对齐强度与图匹配算法找到真实匹配时的有意义对齐强度，为实践者提供判断图匹配质量的实用方法，并给出经验证据与后果探讨。
摘要：
图匹配的对齐强度是一个为实践者提供两图相关性度量的量，它也能让实践者了解图匹配算法是否找到了真实匹配。遗憾的是，当图匹配算法因信号微弱而未能找到真实匹配时，可能会出现“幻影对齐强度”，它源于无意义的匹配，这些匹配由于随机噪声而具有比平均水平更少的不一致（有时少得多）；这种对齐强度可能会给出显著性的误导性外观。实践者需要知道何种水平的对齐强度可能是幻影对齐强度，何种水平表明图匹配算法获得了真实匹配并且是图相关性的有意义度量。这里引入的“幻影对齐强度猜想”提供了一种有原则且实用的方法来处理这一问题。我们为该猜想提供了经验证据，并探讨了其后果。
英文摘要：
The alignment strength of a graph matching is a quantity that gives the practitioner a measure of the correlation of the two graphs, and it can also give the practitioner a sense for whether the graph matching algorithm found the true matching. Unfortunately, when a graph matching algorithm fails to find the truth because of weak signal, there may be "phantom alignment strength" from meaningless matchings that, by random noise, have fewer disagreements than average (sometimes substantially fewer); this alignment strength may give the misleading appearance of significance. A practitioner needs to know what level of alignment strength may be phantom alignment strength and what level indicates that the graph matching algorithm obtained the true matching and is a meaningful measure of the graph correlation. The {\it Phantom Alignment Strength Conjecture} introduced here provides a principled and practical means to approach this issue. We provide empirical evidence for the conjecture, and explore its consequences.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
